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A LOWER BOUND FOR HEILBRONN’S TRIANGLE PROBLEM IN d DIMENSIONS∗
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2001 |
| Abstract | In this paper we show a lower bound for the generalization of Heilbronn’s triangle problem to d dimensions; namely, we show that there exists a set S of n points in the d-dimensional unit cube so that every d + 1 points of S define a simplex of volume Ω( 1 nd ). We also show a constructive incremental positioning of n points in a unit 3-cube for which every tetrahedron defined by four of these points has volume Ω( 1 n4 ). |
| File Format | PDF HTM / HTML |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
